I cant understand why the tan element was needed when it would be easier to just multiply out and then integrate. Can you please explain - i'm really confused. I can follow what you have done, but not why.

I cant understand why the tan element was needed when it would be easier to just multiply out and then integrate. Mr F says: Integrate with respect to what? If you integrate with respect to t, the left hand side is v but the right hand side can't be done because it depends on v. If you integrate with respect to v, the right hand side is easily done byt the left hand side can't be done ..... integral of dv/dt wrt v does not give v!!!

Can you please explain - i'm really confused. I can follow what you have done, but not why.

The differential equation has the generic form . This type of differential equation has to be flipped before any integrating with respect to v can be done. This means that in your question the integration will therefore involve an arctan(v) .....

You have surely learned the technique for solving the generic differential equation .....?